Amen. Easily the best statement on this forum of 2009.
Have mercy on you, o ye of little faith, unbeknownesthththt with the ghhhhospel of Padma. Ye may want to read this:
John Allan Paules - Innumeracy: Mathematical Illiteracy and Its Consequences.
Do you yourself belong to the mathematically illiterate? Let's take a look at the maths of Darski's example:
I sent 5 cavs and 4 Samurai to Paris. One ***Reg*** spear killed 2 cavs, 2 sams and redlined another cav before the 4th cav finally took him out.
As a regular spear has three hit points, it cannot have lost more than (two plus promotions to vet & elite) four rounds of combat whilst winning at least 19 rounds of combat (Darski is not an inexperienced player and would have used at least vet units). Since it was Paris, an AI capital, there would be no defensive bonus from terrain. But the spear was fortified and, for arguments sake, let's assume that Paris was a town, which is what it sounds like from the description given by the mil adviser. This gives the spear a total bonus of 50%, or a defensive combat value of 2+(2x50%)=3. Furthermore, let us assume that the four rounds won by Darski's first four units was divided 3-1 in favour of her cavalry over her samurai. This gives us the following maths:
Per round of combat
Cavalry vs Spearman 6/6+3 = 66.7% cav win, 33.3% spearman win
Samurai vs Spearman 4/4+3 = 57.1% samurai win, 42.9% spearman win
The whole sequence until the 4th cavalry attacked:
Vs cavalry, 14 rounds in all 3 of which was won by the cavalry and 11 by the spearman. This gives an overall ratio of 21.4% against 78.6%,
a statistical deviation greater than 3!
Vs samurai, 9 rounds in all of which the samurai won 1 and the spearman 8 which gives the ratio 11.1% vs 88.9%,
a statistical deviation greater than five!
The mathematical probability of the spearman winning all those rounds works out at 0.000000006424696131 or
1 in 155,649,627. (The probability of winning the lottery is given as a chance of between 1 in 5,200,000 to 1 in 100,000,000.)
Science tells us, provided of course that Darski's recapitulation is factual, that the PRNG of Civ III is not working properly, that is, it does not obey the laws of mathematical probability.
You and Padma would do well to remember the following -
even Nobel Laureate level science starts with a hunch or as you like to term it, "cognitive bias"! When you dismiss it they way you do, it says A LOT about yourselves and your cognitive abilities...
